1. Field of the Invention
The present invention relates generally to a maximum likelihood decoder and a maximum likelihood decoding method, and more particularly, to a device for and a method of maximum-likelihood-decoding a signal vector sequence control-coded to acquire information as it existed before the coding on the signal vector sequence by which noises are reduced.
2. Description of the Background Art
In recent years, digital communication and digital recording and reproduction have been advanced so as to achieve high-quality communication and high-quality recording and reproduction. Maximum likelihood decoding is a decoding method aiming at reducing noises from a digital signal received or reproduced to obtain error-free data in the case of such digital communication and digital recording and reproduction. Consequently, a maximum likelihood detector has been frequently used for an error correcting device, a trellis decoder or the like in a digital communication equipment and a digital recording and reproducing equipment.
FIG. 5 shows a signal vector R.sub.t in a symbol period t and a corresponding code vector P.sub.i,t in an i-th virtual code vector string. In a conventional maximum likelihood decoding method, a metric .left brkt-top.i of the i-th virtual code vector sequence is calculated using the following equation (1) as the square of the magnitude of an error vector, and metrics .left brkt-top.i of virtual code vector sequences corresponding to all paths are found, to obtain information for generating the virtual code vector sequence having the minimum metric .left brkt-top.i as the result of the decoding: ##EQU1##
When the signal vector R.sub.t and the code vector P.sub.i,t are respectively represented as complex numbers by the following equations (2) and (3): EQU R.sub.t =R.sub.xt +jR.sub.yt ( 2) EQU P.sub.i,t =P.sub.xi,t +jP.sub.yi,t ( 3)
the metric .left brkt-top.i of the i-th virtual code vector sequence can be also calculated in accordance with the following equation (4): ##EQU2## In the foregoing equation, t meets the condition of 1.ltoreq.t.ltoreq.n.
In the above described conventional maximum likelihood decoding method, however, a square operation must be performed in finding the metric .left brkt-top.i of the i-th virtual code vector sequence, whereby the scale of an operating circuit becomes large and processing time for the operation becomes long.
Therefore, an object of the present invention is to provide a maximum likelihood decoder having a simple circuit arrangement and capable of performing a high-speed operation and a maximum likelihood decoding method.